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A hierarchical NXFEM for fictitious domain simulations
Université de Pau et des Pays de l'Adour.
University of Sussex Falmer.
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
2011 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 86, no 4-5, 549-559 p.Article in journal (Refereed) Published
Abstract [en]

We suggest a fictitious domain method, based on the Nitsche XFEM method of (Comput. Meth. Appl. Mech. Engrg 2002; 191: 5537-5552), that employs a band of elements adjacent to the boundary. In contrast, the classical fictitious domain method uses Lagrange multipliers on a line (surface) where the boundary condition is to be enforced. The idea can be seen as an extension of the Chimera method of (ESAIM: Math. Model Numer. Anal. 2003; 37: 495-514), but with a hierarchical representation of the discontinuous solution field. The hierarchical formulation is better suited for moving fictitious boundaries since the stiffness matrix of the underlying structured mesh can be retained during the computations. Our technique allows for optimal convergence properties irrespective of the order of the underlying finite element method.

Place, publisher, year, edition, pages
2011. Vol. 86, no 4-5, 549-559 p.
Keyword [en]
Nitsche's method, fictitious domain, extended finite element method
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hj:diva-15811DOI: 10.1002/nme.3093ISI: 000288871900008OAI: oai:DiVA.org:hj-15811DiVA: diva2:440348
Available from: 2011-09-12 Created: 2011-08-16 Last updated: 2012-02-06Bibliographically approved

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Hansbo, Peter
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